Derivation of the threshold pump power of erbium-doped fiber lasers

Starting from the rate equations describing the interaction between a three-level atom and a two-wavelength field appropriate to the erbium-doped fiber lasers pumped by 980-nm light, we establish an analytical and explicit expression for the threshold pump power of the laser. From this it is then shown that a relationship between the threshold power and other primary system parameters can be quantitatively specified.